Abstract

High-frequency components that are lost when a signal
s(x) of bandwidth W is low-pass filtered in
sinusoid-crossing sampling are recovered by use of the
minimum-negativity constraint. The lost high-frequency components
are recovered from the information that is available in the Fourier
spectrum, which is computed directly from locations of intersections
{xi} between s(x) and
the reference sinusoid r(x) = Acos(2πfrx), where the index
i = 1, 2, … , 2M = 2Tfr, and
T is the sampling period. Low-pass filtering occurs when
fr < W/2. If |s(x)| ≤
A for all values of x within T, then a
crossing exists within each period Δ =
1/2fr. The recovery procedure is investigated
for the practical case of when W is not known a
priori and s(x) is corrupted by additive Gaussian
noise.

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